Diffuser plate

ABSTRACT

A transmission-type or reflection-type diffuser plate including a planar base material on which an optical element having an effective diameter of “a” in an X-axis direction and an effective diameter of “b” in a Y-axis direction is provided to constitute an a×b two-dimensional basic periodic structure, each of the basic periodic structure having an Na×Mb two-dimensional periodic phase structure in which a basic block has N rows and M columns including N optical elements in the X-axis direction and M optical elements in the Y-axis direction, the diffuser plate being configured such that if a phase structure P nm  in the n-th row and the m-th column is expressed by P n1 +P 1m , and directivity is represented by square of the absolute value of Fourier transform of complex transmittance or complex reflectance of an optical element in the n-th row and the m-th column in the basic block; a ratio of standard deviation to average of the directivity is 0.3 or less.

TECHNICAL FIELD

The present invention relates to a diffuser plate.

BACKGROUND ART

There have been proposed techniques for applying, as a screen, adiffuser plate that uses a microlens array to a head-up display, a laserprojector, etc. Advantages that can be obtained by use of a microlensarray may include suppression of speckle noise as compared to a casewhere a diffuser plate such as an opaque plate or opaque glass is used.

For example, Patent Literature 1 proposes an image forming apparatuswhich includes a laser projector that uses laser light as a light sourceand is adapted to project an image formed by an array of a plurality ofpixels, and a diffuser plate that uses a microlens array in which aplurality of microlenses are arranged. If a microlens array is used,incident light can be appropriately diffused, and a necessary diffusionangle can be freely designed.

Patent Literature 2 proposes a method for mitigating unevenness ofluminance or unevenness of color due to the diffracted light caused byperiodicity of the microstructure through random distribution of atleast one of the parameters defining the shape or position of themicrostructure of a microlens and the like in accordance with apredetermined probability density function.

Patent Literatures 3 and 4 propose methods for making it possible tocreate new diffracted light in the gap between traditional diffractedlight by imparting, to the microlens array, a second periodic structurethat has the functionality of creating an optical path length differencefor the light transmitted through the individual microlenses, andthereby mitigate the unevenness of luminance or unevenness of color.

CITATION LIST Patent Literature

-   Patent Literature 1: Japanese Unexamined Patent Application    Publication No. 2010-145745-   Patent Literature 2: Published Japanese Translation of PCT    International Publication for Patent Application, No. 2004-505306-   Patent Literature 3: International Patent Publication No.    2016/139769-   Patent Literature 4: Japanese Unexamined Patent Application    Publication No. 2017-122773

SUMMARY OF INVENTION Technical Problem

When a typical microlens array is used, unevenness of luminance occursdue to diffraction spots caused by the periodicity of the microlensarray. Patent Literature 2 describes that unevenness of luminance can bemitigated by causing at least one of the parameters defining the shapeor position of the lens to be randomly distributed in accordance with apredetermined probability density function. However, if randomness isimparted to the shape and/or position of the lens as in PatentLiterature 2, a problem arises that speckle noise is likely to occur andthe image quality is deteriorated because a random phase differenceoccurs in the light transmitted through the lens array. Moreover, whilethe random distribution mitigates the unevenness of luminance as anoverall average of the microlens array, another problem arises that aportion left unmitigated may exist locally.

Patent Literatures 3 and 4 describe that the unevenness of luminance ismitigated by imparting a second periodic structure, which has afunctionality of creating an optical path length difference for thelight transmitted through the individual microlenses, to the microlensarray. However, according to the periodic structures defined bystaggered arrangement or two vertical axes as proposed in PatentLiteratures 3 and 4, since the density of diffracted light increasesonly several times, and differences in luminance occur among theindividual diffracted light, there may be a case where unevenness ofluminance cannot be sufficiently mitigated.

It is an object of the present invention to provide a diffuser platethat can further mitigate unevenness of luminance or unevenness of colorwhile suppressing speckle noise of transmitted light or reflected light.

Solution to Problem

The present invention achieves the above-described object by theconfiguration described below.

[1] A transmission-type or reflection-type diffuser plate, including

a planar base material on which an X-axis and a Y-axis which areorthogonal to each other are defined in a plane direction, in which

-   -   an optical element having an effective diameter of “a” in an        X-axis direction, and an effective diameter of “b” in a Y-axis        direction is provided on one surface of the planar base        material; or    -   a first optical element having an effective diameter of “a” in        the X-axis direction is provided on one surface of the planar        base material, and a second optical element having an effective        diameter of “b” in the Y-axis direction is provided on the other        surface of the planar base material, and an optical element        having an effective diameter of “a” in the X-axis direction, and        an effective diameter of “b” in the Y-axis direction is formed        by combining the first optical element and the second optical        element;

an a×b two-dimensional basic periodic structure is constituted by aplurality of the optical elements being disposed in the X-axis directionand the Y-axis direction at intervals respectively based on theeffective diameters;

each basic periodic structure has a structure that creates an opticalpath length difference, respectively;

the structure that creates the optical path length difference has anNa×Mb two-dimensional periodic phase structure in which a basic blockhas N rows and M columns (at least one of M and N is an integer of 3 ormore) including N optical elements in the X-axis direction and M opticalelements in the Y-axis direction; and

the diffuser plate is configured such that

if a phase structure in the n-th row and the m-th column in the basicblock is denoted by P_(nm), and if a basic periodic phase differenceΔP_(X) in the X-axis direction and a basic periodic phase differenceΔP_(Y) in the Y-axis direction are represented by the followingexpressions (1) and (2), the P_(nm) is expressed as P_(n1)+P_(1m); and

ΔP _(X)=(P ₁₁ P ₂₁ . . . P _(N1))  Expression (1)

ΔP _(Y)=(P ₁₁ P ₁₂ . . . P _(1M))  Expression (2)

if complex transmittance or complex reflectance of the optical elementin the n-th row and the m-th column in the basic block is denoted byg(n/λ, m/λ), and directivity is represented by square of the absolutevalue of Fourier transform G(sin θ_(n), sin θ_(m)) of complextransmittance or complex reflectance, a ratio of standard deviation toaverage of the directivity expressed by the following expression (3) is0.3 or less.

$\begin{matrix}\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( {{{G_{N,M}\left( {{\sin\;\theta_{n}},{\sin\;\theta_{m}}} \right)}}^{2} - {Ave}} \right)^{2}}}}}{Ave} & {{Expression}\mspace{14mu}(3)}\end{matrix}$

(In the expression (3), Ave is an average value of |G(sin θ_(n), sinθ_(m))|² of each optical element in the basic block.)

[2] The diffuser plate according to [1], in which the ratio of thestandard deviation to the average of the directivity expressed by theexpression (3) is 0.1 or less.[3] The diffuser plate according to [1], in which the ratio of thestandard deviation to the average of the directivity expressed by theexpression (3) is 0.[4] The diffuser plate according to any one of [1] to [3], in which

the N and M are each independently any of 3, 4, 5, 7, and 8, and when awavelength of incident light is λ,

a basic periodic phase difference ΔP_(X) in the X-axis direction and abasic periodic phase difference ΔP_(Y) in the Y-axis direction areindependently one of the following ΔP_(A).

${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & {\frac{1}{3}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & 0 & {\frac{2}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & 0 & {\frac{3}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{1}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & 0 & {\frac{2}{5}\lambda} & {\frac{2}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{1}{5}\lambda} & 0 & {\frac{3}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{1}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{2}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{1}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{2}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & 0 & {\frac{4}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{4}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{1}{7}\lambda} & 0 & {\frac{5}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{5}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{1}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{1}{7}\lambda} & 0 & {\frac{2}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{0}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{2}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{2}{7}\lambda} & 0 & {\frac{3}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & 0 & {\frac{4}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & 0 & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & 0 & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & {\frac{2}{8}\lambda} & 0 & 0 & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & 0 & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & 0 & {\frac{7}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{7}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{5}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{1}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{3}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{7}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{7}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{5}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{1}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & 0 & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & 0 & {\frac{6}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{6}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{6}{8}\lambda} & 0 & {\frac{6}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & 0 & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{3}{8}\lambda} & 0 & {\frac{7}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{7}{8}\lambda}\end{pmatrix}$

[5] The diffuser plate according to [4], in which the λ is 630 nm.

[6] The diffuser plate according to [4], in which the λ is 530 nm.

[7] The diffuser plate according to [4], in which the λ is 580 nm.

Advantageous Effects of Invention

According to the present invention, it is possible to provide a diffuserplate which can mitigate unevenness of luminance or unevenness of colorwhile suppressing speckle noise of transmitted light or reflected light.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic front view that illustrates a diffuser plateaccording to a first embodiment.

FIG. 2 is a 1A-1A′ sectional view in the diffuser plate of FIG. 1.

FIG. 3 is a 1B-1B′ sectional view in the diffuser plate of FIG. 1.

FIG. 4 is a front view and a side view that illustrate a basic block ina diffuser plate according to a second embodiment.

FIG. 5 is a 4A-4A′ sectional view in the basic block of FIG. 4.

FIG. 6 is a 4B-4B′ sectional view in the basic block of FIG. 4.

FIG. 7 is a sectional view that illustrates a modified example of thediffuser plate of FIG. 1.

FIG. 8 is a perspective view that illustrates an example of a microlenswhich is an optical element.

FIG. 9 is a diagram that illustrates a result of diffracted lightsimulation of a microlens array having a 20 μm×20 μm pitch.

FIG. 10 is a diagram that illustrates a result of diffracted lightexperiment of a microlens array having a 40 μm×40 μm pitch.

FIG. 11 is a diagram that illustrates a result of diffracted lightsimulation of a microlens array having a 20 μm×20 μm pitch.

FIG. 12 is a diagram that illustrates a result (comparative example) ofdiffracted light simulation of a microlens array having a 20 μm×20 μmpitch.

DESCRIPTION OF EMBODIMENTS

Embodiments of a diffuser plate according to the present invention willbe described with reference to the drawings. However, the presentinvention is not limited to the following embodiments. Further, in orderto clarify the explanation, the following description and drawings areappropriately simplified, and scaling of each axial direction may bedifferent. In addition, terms such as “parallel”, “vertical”,“orthogonal”, and “identical” that specify shapes, geometric conditions,and degrees thereof as used in the present specification shall beinterpreted to include a range in which similar functions can beexpected, without being bound to a strict meaning.

First Embodiment

Referring to FIGS. 1 to 3, a diffuser plate according to a firstembodiment will be described. FIG. 1 is a schematic front view thatillustrates a diffuser plate according to the first embodiment. FIG. 2is a 1A-1A′ sectional view in the diffuser plate of FIG. 1, and FIG. 3is a 1B-1B′ sectional view in the diffuser plate of FIG. 1. Note that inthe examples of FIGS. 1 to 3, N=M=4.

A diffuser plate 100 of the first embodiment is a transmission-typediffuser plate, and has a plurality of optical elements 53 having aneffective diameter of “a” in an X-axis direction, and an effectivediameter of “b” in a Y-axis direction on one surface (+Z side surface)of a planar base material 51.

The plurality of optical elements 53 are arranged in the X-axisdirection and the Y-axis direction at intervals based on the respectiveeffective diameters, thereby constituting an a×b two-dimensional basicperiodic structure 10 in which each optical element 53 is one unit.

Each of the plurality of basic periodic structures 10 has a structurethat creates an optical path length difference. In the presentembodiment, as an example of a structure that creates an optical pathlength difference, a predetermined raised portion 52 is provided betweenthe planar base material 51 and the optical element 53. The raisedportion 52 has a periodic phase structure of N optical elements (thatis, Na) in the X-axis direction, and has a periodic phase structure of Moptical elements (that is, Mb) in the Y-axis direction.

In the present embodiment, through a combination of the periodic phaseshift structure in the X-axis direction and the periodic phase shiftstructure in the Y-axis direction, an Na×Mb two-dimensional periodicphase structure is formed in which a basic block 50 has N rows and Mcolumns.

Specifically, when the phase structure in the n-th row and the m-thcolumn in the basic block 50 is denoted by P_(nm), and a periodic phasedifference ΔP_(X) in the X-axis direction and a periodic phasedifference ΔP_(Y) in the Y-axis direction are expressed by the forms ofthe following expressions (1) and (2), the P_(nm) is expressed byP_(n1)+P_(1m).

ΔP _(X)=(P ₁₁ P ₂₁ . . . P _(N1))  Expression (1)

ΔP _(Y)=(P ₁₁ P ₁₂ . . . P _(1M))  Expression (2)

Although the details of the periodic phase structure will be describedlater, the diffuser plate of the present embodiment suppresses specklenoise by giving a periodic predetermined phase difference to each lighttransmitted through each optical element 53. Further, the diffuser plateof the present embodiment is configured such that at least one of N andM is an integer of 3 or more so that the unevenness of luminance and theunevenness of color are further mitigated.

FIG. 2 is a sectional view that illustrates an example of a crosssection passing through the basic periodic structures 11, 21, 31 and 41along the X-axis. As shown in the example of FIG. 2, in the diffuserplate 100, optical elements 53 each having an effective diameter “a” inthe X-axis direction are arranged at intervals based on the effectivediameter to form basic periodic structures 11 to 41 in the X-axisdirection. Each basic structure has a raised portion 52 for creating anoptical path length difference. The raised portion 52 forms a repeatingperiodic phase structure with Na including N optical elements as aperiod. Here, a thickness T of the planar base material 51 is themaximum thickness that can be regarded as flat. Specifically, thethickness is from the surface having no optical element 53 to the rootof the optical element 53 having the minimum height in the basic block50 (the optical element 53 in the basic periodic structure 11 in theexample of FIG. 2). The optical path differences 71 and 72 are based onthe optical element having the minimum height.

FIG. 3 is a sectional view that illustrates an example of a crosssection passing through the basic periodic structures 14, 13, 12 and 11along the Y-axis. As shown in the example of FIG. 3, in the diffuserplate 100, optical elements 53 having an effective diameter b in theY-axis direction are arranged at intervals based on the effectivediameter to constitute the basic periodic structures 14 to 11. Eachbasic structure has a raised portion 52 for creating an optical pathlength difference. The raised portion 52 forms a repeating phasestructure with Mb including M optical elements as a period.

The shape of the optical element 53 is not particularly limited, and ashape of a lens that serves as a reference is designed from opticalphysical properties (particularly, refractive index) of the material tobe used for the diffuser plate 100 and a desired diffusion angledistribution. The shape of the lens may be spherical or aspherical.Optical design is performed using conventional techniques such as theray tracing method. Further, this is not limiting when it is desired togive anisotropy to the diffusion characteristics, and the aspect ratioof the lens can be arbitrarily set. A typical example is a quadrangularmicrolens as shown in FIG. 8. Further, it may be a concave lens whichhas an inverted shape of the microlens (see FIG. 7).

Next, details of the periodic phase structure will be described togetherwith the principle thereof.

(Principle of Optical Path Length Difference Set Between OpticalElements)

When parallel light (wavelength λ) is incident on a microlens array inwhich square lenses having an effective diameter of L are arranged witha period of L, if there is no structure that creates an optical pathlength difference in each lens, the luminance distribution of theemitted light is discretized in the vertical and horizontal directionsat a sine interval λ/L (called diffracted light) due to the well-knowndiffraction grating action. When the incident light is not parallellight but has a conical shape with an apparent diameter of ω, eachdiscretized direction has a conical shape with an apparent diameter ofω. When ω is larger than the 2λ/L value, the discretized state issubstantially eliminated. However, when w is smaller than 2λ/L, theperiodicity of the sinusoidal interval λ/L remains in the luminancedistribution as a remnant of discretization, which causes unevenness ofluminance between light and dark.

FIG. 9(a) shows a simulation result of diffracted light transmittedthrough a microlens array with a 20 μm×20 μm period, which has nostructure that creates an optical path length difference. As describedabove, when each lens does not have a structure that creates an opticalpath length difference, diffracted light that is discretized in thevertical and horizontal directions with a sine interval λ/L isgenerated.

Further, FIG. 10(a) shows an image obtained by making laser lightactually incident on a microlens array with a 40 μm×40 μm period, whichdoes not have a structure that creates an optical path lengthdifference, and projecting the emitted light onto a vertical plane. Asshown in FIG. 10(a), the laser light actually emitted is discretized,which is in good agreement with the simulation result of FIG. 9(a).

To overcome this unevenness of luminance, it is necessary to reduce theinterval of diffracted light. As a solution to this problem, there is amethod of providing a structure that creates an optical path lengthdifference in the light incident on each lens. In the presentembodiment, let us consider to provide a structure that creates anoptical path length difference with a period of N lenses in the X-axisdirection and M lenses in the Y-axis direction (at least one of N and Mis an integer of 3 or more), and to add the sum of the optical pathlength difference included in the periodic phase structure of the X-axisdirection and the optical path length difference included in theperiodic phase structure of the Y-axis direction to the incident light.Creating an optical path length difference in an actual microlens can berealized by arranging the microlenses at different positions in theZ-axis direction by providing raised portions 52, for example, as shownin FIG. 2.

Here, if complex transmittance of the optical element 53 in the n-th rowand the m-th column in the basic block 50 is denoted by g(n/λ, m/λ),directivity of the emitted light matches the square of the absolutevalue of Fourier transform G(sin θ_(n), sin θ_(m)) thereof. Thismatching relationship also holds for all the optical elements arrangedperiodically.

Further, the same thing holds for a two-dimensional periodic array ofbasic block 50 with a unit g_(N, M)(n/λ, m/λ), which collectivelyincludes N lenses in the X-axis direction and M lenses in the Y-axisdirection. Therefore, the target directivity |G_(N, M)(sin θ_(n), sinθ_(m))|² is a discrete structure having an angular period of λ/(Na) inthe X-axis direction and λ/(Mb) in the Y-axis direction, and itsenvelope is proportional to the directivity |G(sin θ_(n), sin θ_(m))|²of a single lens.

Therefore, by applying the Na×Mb two-dimensional periodic phasestructure, the angular period of the diffracted light can be reduced to1/N in the X-axis direction and to 1/M in the Y-axis direction. Further,the unevenness of luminance is mitigated most under a condition thatintensities of all the diffracted light are uniform. That is, thecondition that the standard deviation of each element of |G_(N, M)(sinθ_(n), sin θ_(m))|², which is the directivity of the emitted light, is 0is the best. Therefore, if the average value of each element of|G_(N, M)(sin θ_(n), sin θ_(m))|² is denoted by Ave, the smaller thefollowing expression (4) is, the more preferable it is, and it is themost preferable when the expression (4) is 0.

$\begin{matrix}\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( {{{G_{N,M}\left( {{\sin\;\theta_{n}},{\sin\;\theta_{m}}} \right)}}^{2} - {Ave}} \right)^{2}}}} & {{Expression}\mspace{14mu}(4)}\end{matrix}$

The condition that the above-described expression (4) is 0 is an idealcondition in which the intensities of all diffracted light are uniform,but in reality, some unevenness of luminance may be allowed. In thepresent embodiment, if the standard deviation of each element ofG_(N, M)(sin θ_(n), sin θ_(m)), which is the directivity of the emittedlight, is 30% of the average value or less, it is judged that theunevenness of luminance is suppressed. That is, in the diffuser plateaccording to the present embodiment the ratio of the standard deviationto the average of the directivity represented by the followingexpression (3) is characteristically 0.3 or less, preferably 0.1 orless, and more preferably 0.

$\begin{matrix}\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( {{{G_{N,M}\left( {{\sin\;\theta_{n}},{\sin\;\theta_{m}}} \right)}}^{2} - {Ave}} \right)^{2}}}}}{Ave} & {{Expression}\mspace{14mu}(3)}\end{matrix}$

(In the expression (3), Ave is an average value of |G(sin θ_(n), sinθ_(m))|² of each optical element in the basic block.)

Conventionally, it has been known an example that the expression (3) is0.3 or less only for N=M=2 (Patent Literature 4). According to thepresent embodiment, it is possible to provide a microlens array in whichthe expression (3) is 0.3 or less even for N, M≥3 or more. In order tomake the unevenness of luminance due to the diffracted light of amicrolens array inconspicuous, it is necessary to make the apparentdiameter ω of the incident light larger than 2λ/(2 L) when N=M=2. WhenN=M=3, the apparent diameter ω of the incident light needs to be largerthan 2λ/(3 L). Therefore, when N=M=3, it is permissible to reduce theapparent diameter ω of the incident light to ⅔ times as large as that inthe case of N=M=2. Alternatively, the L value itself can be reduced toincrease a resolution limit of the microlens array by 1.5 times.Therefore, if the present invention is used, a diffuser plate havinghigher efficiency than that of the conventional art can be obtained.

As an example, the case of N=M=4 shown in the examples of FIGS. 1 to 3will be described in detail. Let P_(nm) be a phase structure in the n-throw and the m-th column in the basic block. Consider the case where eachlens does not have a structure that creates an optical path lengthdifference. At this time, assuming that the phase difference for oneperiod of the periodic phase structure is ΔP, ΔP is expressed asfollows:

${\Delta\; P} = \begin{pmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{pmatrix}$

At this time, the complex transmittance g(n/λ, m/λ) is given as follows:

$g = \begin{pmatrix}1 & 1 & 1 & 1 \\1 & 1 & 1 & 1 \\1 & 1 & 1 & 1 \\1 & 1 & 1 & 1\end{pmatrix}$

The square of the absolute value of Fourier transform G (sin θ_(n), sinθ_(m)) of the above-described g(n/λ, m/λ) is given as follows:

${G}^{2} = {\begin{pmatrix}256 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{pmatrix}.}$

A ratio of the standard deviation to the average is obtained from this|G|² as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}{\sum\limits_{1}^{N}\;\left( \;{{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = {3.87.}$

Therefore, when no raised portion 52 is provided, the condition that theexpression (3) is 0.3 or less is not satisfied.

Next, consider the case where the lens has a raised portion 52 thatcreates an optical path length difference at N=M=4. Here, supposing asan example that the phase structure in the n-th row and the m-th columnin the basic block is P_(nm), a basic periodic phase difference ΔP_(X)in the X-axis direction and a basic periodic phase difference ΔP_(Y) inthe Y-axis direction are set as follows.

${\Delta\; P_{X}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{Y}} = {\begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda}\end{pmatrix}.}$

Here, if it is assumed that P_(nm) is P_(n1)+P_(1m), the periodic phasestructure ΔP of the basic block is expressed as follows:

$\begin{matrix}{{\Delta\; P} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda} \\{\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{3}{4}\lambda} & {\frac{2}{4}\lambda} \\{\frac{2}{4}\lambda} & {\frac{3}{4}\lambda} & \lambda & {\frac{3}{4}\lambda} \\{\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{3}{4}\lambda} & {\frac{2}{4}\lambda}\end{pmatrix}} & {{Expression}\mspace{14mu}(5)}\end{matrix}$

At this time, the Fourier transform G (sin θ_(n), sin θ_(m)) of g(n/λ,m/λ) is as follows:

$g = {\begin{pmatrix}1 & {\exp\left( \frac{i\;\pi}{2} \right)} & {\exp\;\left( {i\;\pi} \right)} & {\exp\left( \frac{i\;\pi}{2} \right)} \\{\exp\left( \frac{i\;\pi}{2} \right)} & {\exp\;\left( {i\;\pi} \right)} & {\exp\left( \frac{3i\;\pi}{2} \right)} & {\exp\;\left( {i\;\pi} \right)} \\{\exp\;\left( {i\;\pi} \right)} & {\exp\left( \frac{3i\;\pi}{2} \right)} & 1 & {\exp\left( \frac{3i\;\pi}{2} \right)} \\{\exp\left( \frac{i\;\pi}{2} \right)} & {\exp\;\left( {i\;\pi} \right)} & {\exp\left( \frac{3i\;\pi}{2} \right)} & {\exp\;\left( {i\;\pi} \right)}\end{pmatrix}.}$

The square of the absolute value of G (sin θ_(n), sin θ_(m)) obtained byFourier transforming the g(n/λ, m/λ) is as follows:

${G}^{2} = \begin{pmatrix}16 & 16 & 16 & 16 \\16 & 16 & 16 & 16 \\16 & 16 & 16 & 16 \\16 & 16 & 16 & 16\end{pmatrix}$

This represents that the emission angle of the diffracted light isevenly divided into 16 parts, that is, the diffracted light density willincrease by 16 times. From this |G|², the ratio of the standarddeviation to the average is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}{\sum\limits_{1}^{N}\;\left( \;{{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 0.$

Therefore, it has been confirmed that the condition that the expression(3) is 0.3 or less is satisfied. The phase difference satisfying theexpression (3) with N=M=4 is not limited to the expression (5), and anyphase difference can be set as long as the condition that the expression(3) is 0.3 or less is satisfied. Further, even when N and M are otherthan 4, any phase difference which satisfies the condition that theexpression (3) is 0.3 or less may be set. Further, N and M do not haveto be the same value, and may be set to different values such as N=3 andM=4.

As a specific example, the N and M are independently any of 3, 4, 5, 7or 8, and when the wavelength of the incident light is λ, if the basicperiodic phase difference ΔP_(X) in the X-axis direction and the basicperiodic phase difference ΔP_(Y) in the Y-axis direction areindependently any of the following ΔP_(A), the value of the expression(3) will be 0. Note that although it is possible to set N and M to 9 ormore, since there are many examples, these will not be shown.

${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & {\frac{1}{3}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & 0 & {\frac{2}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & 0 & {\frac{3}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{1}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & 0 & {\frac{2}{5}\lambda} & {\frac{2}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{1}{5}\lambda} & 0 & {\frac{3}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{1}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{2}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{1}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{2}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & 0 & {\frac{4}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{4}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{1}{7}\lambda} & 0 & {\frac{5}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{5}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{1}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{1}{7}\lambda} & 0 & {\frac{2}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{0}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{2}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{2}{7}\lambda} & 0 & {\frac{3}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & 0 & {\frac{4}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & 0 & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & 0 & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & {\frac{2}{8}\lambda} & 0 & 0 & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & 0 & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & 0 & {\frac{7}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{7}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{5}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{1}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{3}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{7}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{7}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{5}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{1}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & 0 & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & 0 & {\frac{6}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{6}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{6}{8}\lambda} & 0 & {\frac{6}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & 0 & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{3}{8}\lambda} & 0 & {\frac{7}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{7}{8}\lambda}\end{pmatrix}$

FIG. 9(b) shows a simulation result of diffracted light transmittedthrough a microlens array with a 20 μm×20 μm period, which has astructure that creates an optical path length difference of theexpression (5). As shown in the above calculation result, it can beconfirmed that the density of the diffracted light has increased by 16times compared with that in FIG. 9(a), and the unevenness of luminanceis reduced. Further, FIG. 10(b) shows an image obtained by making theemitted light of the laser light incident on the microlens array with anactual 40 μm×40 μm period, which has a structure that creates an opticalpath length difference of the expression (5), and projecting the emittedlight onto a vertical plane. In order to create an optical path lengthdifference corresponding to the expression (5) in this microlens array,a height difference ΔH is imparted to the lens height. In atransmission-type diffuser plate, when the refractive index of thematerial constituting the microlens array is 1.5 and the wavelength λ ofthe light source used is 630 nm red light, which has the longestwavelength within the visible light, the ΔH is as shown below:

${\Delta\; H} = \begin{pmatrix}0 & {0.315\mspace{14mu}{µm}} & {0.63\mspace{14mu}{µm}} & {0.315\mspace{14mu}{µm}} \\{0.315\mspace{14mu}{µm}} & {0.63\mspace{14mu}{µm}} & {0.945\mspace{14mu}{µm}} & {0.63\mspace{14mu}{µm}} \\{0.63\mspace{14mu}{µm}} & {0.945\mspace{14mu}{µm}} & 0 & {0.945\mspace{14mu}{µm}} \\{0.315\mspace{14mu}{µm}} & {0.63\mspace{14mu}{µm}} & {0.945\mspace{14mu}{µm}} & {0.63\mspace{14mu}{µm}}\end{pmatrix}$

As shown in FIG. 10(b), the density of the emitted laser light hasincreased by 16 times, which is in good agreement with the simulationresult.

Even when the wavelength λ of the light source used is 530 nm greenlight, which has the highest visibility in the visible light, or 580 nmyellow light, which has an intermediate wavelength between red lighthaving the longest wavelength and green light having the highestvisibility in the visible light, it is possible to determine the ΔH tobe imparted, in the same manner.

When light is incident on the entire microlens array, the density ofdiffracted light increases as N and M, which are the numbers of lensescorresponding to one period of the periodic phase structure, increase.Therefore, in general, the larger N and M are, the greater the effect ofreducing the unevenness of luminance, which is preferable. On the otherhand, when the lens region in which light is incident is limited, it ispreferable to adjust the size of one period of the periodic phasestructure to the lens region. For example, when diffusing the laser beamlight that is not scanned, the size of one period of the periodic phasestructure may be set to about the size of the laser beam diameter.However, when the laser beam light is scanned over the entire microlensarray, the larger N and M are, the more preferable it is as describedabove.

Next, the method for setting the phase difference will be described. Inthe present invention, the phase difference is represented using thedifference in the optical path length of the light transmitted throughor reflected by the microlens, where the difference is normalized byusing the wavelength. To change the phase difference, various factorssuch as lens height, curvature, pitch, arrangement, and refractive indexcan be selected. The present embodiment is characteristic in that toimpart a phase difference to each lens, only the height of the raisedportion 52 of the lens is changed, whilst the curvatures of theindividual lenses are substantially the same.

In the present embodiment, as shown in FIGS. 2 to 3, the individuallenses are made to have the same cross section profile, and the heightof the raised portion 52 is controlled to change a convex portionmaximum height of the microlens. That is, the convex portion maximumheight of the microlens is determined by the sum of the lens height ofthe optical element 53 determined by optical design and the height ofthe raised portion 52. In the present invention, the lens height is afixed value, and the height of the raised portion 52 is changed amongthe individual lenses to create a phase difference in each microlens, soas to mitigate the unevenness of luminance and unevenness of colorcaused by diffraction-related factors. When the height difference of theconvex portion maximum height of each microlens is denoted by ΔH, andwhen the refractive index of the material constituting the microlensarray is denoted by “n” and the wavelength of the light source to beused is denoted by λ, [nm], the phase difference corresponding to ΔH isexpressed as:

{1000×ΔH×(n−1)}/λ

Here, when the light source includes a plurality of wavelengths, thecalculation may be performed with the longest wavelength or thewavelength with the highest visibility as representative one among thewavelengths to be used.

As a modified example of the above-described first embodiment, FIG. 7shows an example of a 1A-1A′ sectional view in the case of a concavelens. The shape of the optical element 53 is different from that of thefirst embodiment. Although a 1B-1B′ sectional view is not shown, theoptical element 53 also has a concave lens shape having an effectivediameter of b.

The optical path difference in the case of a concave lens may beconsidered by replacing the above-described ΔH with a height differenceΔD of the concave portion maximum depth of each microlens.

Further, as a modified example of the above-described first embodiment,a reflection-type diffuser plate may be used (not shown). Areflection-type diffuser plate can be manufactured by forming areflective film such as an aluminum vapor deposition film on the surfaceof the optical element side or the opposite side of the diffuser plateof the first embodiment.

If the optical element has a convex lens shape in a reflection-typediffuser plate, incident light is reflected on the surface of themicrolens having distribution in the convex portion maximum height, andoptical path difference of light passing through the air occurs,resulting in a phase difference between the individual microlenses. Thephase difference corresponding to the maximum height difference ΔH ofthe convex portion maximum height between the individual microlenses atthis point is expressed by:

{1000×2ΔH}/λ

Where, if the light source includes a plurality of wavelengths, then, inthe same manner as in the case of a transmission type, the calculationmay be performed with the longest wavelength or the wavelength with thehighest visibility as representative one among the wavelengths to beused.

Moreover, in the case of the reflection-type diffuser plate, the partthat is defined as “complex transmittance” in the principle of theoptical path length difference set between the optical elementsdescribed above can be similarly considered by reading it as “complexreflectance” and thus it is possible to design a structure that createsan optical path length difference.

Further, when the optical element has a concave lens shape in thereflection-type diffuser plate, the same discussion can be applied as inthe case of the transmission type, in which the maximum heightdifference ΔD of the concave portion maximum depth of the individualmicrolenses is considered in place of the ΔH.

As the method for processing the microlens array based on the designdata, various processing methods can be used such as mechanicalprocessing, photolithography using a mask, maskless lithography,etching, and laser ablation. A mold is manufactured using thesetechniques, and a resin is molded to manufacture a diffuser plate memberhaving a microlens array. The same mold may be used as a directreflection-type diffuser plate. The molding method should be selected asappropriate from various molding techniques such as roll-to-rollmolding, hot press molding, molding using ultraviolet curable resin,injection molding, and the like. If the diffuser plate member is to beused as a reflection-type diffusion component, then it should be usedwith a reflective film such as aluminum vapor deposition film formed onits front or back surface.

Hereinafter, as an example, a method for producing a mold by laserscanning maskless lithography and electroforming, and molding a diffuserplate by hot press molding using the mold will be described in moredetail.

Maskless lithography includes a resist coating step of coating aphotoresist on a substrate, an exposure step of exposing a fine patternto the photoresist, and a development step of developing the photoresistthat has been subjected to the exposure to obtain an original componenthaving the fine pattern. In the resist coating step, a positivephotoresist is coated on the substrate. The thickness of the coatingfilm of the photoresist should be equal to or greater than the height ofthe fine pattern. It is preferable that the coating film is subjected toa baking process at 70 to 110° C. In the exposure step, the photoresistcoated in the coating step is irradiated with a laser beam while it isbeing scanned by the laser beam so as to expose the photoresist. Thewavelength of the laser beam may be selected according to the type ofthe photoresist and, for example, 351 nm, 364 nm, 458 nm, 488 nm(oscillation wavelength of Ar⁺ laser), 351 nm, 406 nm, 413 nm(oscillation wavelength of Kr⁺ laser), 352 nm, 442 nm (oscillationwavelength of He—Cd laser), 355 nm, 473 nm (pulse oscillation wavelengthof diode-pumped solid-state laser), 375 nm, 405 nm, 445 nm, 488 nm(semiconductor laser), and the like can be selected.

In the exposure step of a microlens having a raised portion, the resistis scanned by the laser while the laser power is modulated to a valuedetermined by the shape of the lens and the resist sensitivity. Thelaser used in the laser exposure is focused by an objective lens tofocus on the resist. In order to increase the difference in the heightof raising between a certain microlens and another lens adjacentthereto, the difference in laser power between the microlenses adjacentto each other should be increased. However, since the laser spotgenerally exhibits a Gaussian distribution with a finite diameter,excessive increase in the difference in the laser power causes increasein the areas where the lens shape near the boundary between the adjacentlenses deviates from the shape specified based on the optical design,reducing the proportion of the lens sections where the diffusion angledistribution is the same as those of the other lenses. Accordingly, inorder to obtain the same diffusion angle distribution as that of theoptical design, it is preferable to keep the height difference of theraised portion between the adjacent microlenses within a certain range.According to the present invention, since the heights of the lensportions of the individual microlenses are constant, the maximum heightdifference ΔH of the convex portion maximum height of the individualmicrolenses agrees with the maximum height difference of the height ofraising. Accordingly, it is preferable to set the height of raising sothat the phase difference normalized by the aforementioned wavelengthfalls within the range of 0 to 1.

In the development step, the photoresist that has been subjected to theexposure is developed. The development of the photoresist can be carriedout by a known method. The developer is not particularly limited, and analkali developer such as tetramethylammonium hydroxide (TMAH) can beused. In the development step, the photoresist is removed according tothe exposure amount, and the fine pattern shape of the photoresist isformed. If a positive resist is used in the exposure step and theexposure is carried out with the laser power according to the shape ofthe microlens configured by a concave lens, then an original microlenscomponent with the concave lens formed on the photoresist is obtained.

Next, in the electroforming step, the surface of the photoresist havingthe fine pattern that has been formed by the exposure and thedevelopment is subjected to a conductivity treatment by a method such asvapor deposition of nickel metal. Further, nickel is deposited on thesurface of the vapor-deposited film in a plate shape with a desiredthickness by electroforming and, when this nickel plate is peeled fromthe photoresist original component, a die (stamper) will be obtained inwhich the microlens array based on a convex lens is formed with theconcave lens shape of the photoresist has been inverted and transferred.

In the molding step, the convex lens-shaped fine pattern is transferredto an acrylic sheet by a hot press method in which the acrylic sheet ispressed while being heated using the above-described stamper. As aresult, it is made possible to manufacture a microlens array memberusing a concave lens. If double-sided molding with stampers arranged onboth sides is adopted, it is also possible to mold a member with amicrolens array formed on both sides. The resin used in the molding isnot limited to acrylic, and a resin that can be used for the diffuserplate should be selected according to the molding conditions. In orderto obtain a microlens array member configured by a convex lens,electroforming duplication is carried out using, as the mold, thestamper (convex lens) that has been obtained in the above-describedelectroforming step, and a stamper with a microlens array formed using aconcave lens is produced, and this stamper should be used to perform hotpress molding. Whilst it will be appreciated that a method for exposingthe resist by modulating the exposure power according to the convex lensin the exposure step of the maskless lithography can be adopted, theabove-described method for performing electroforming duplication of thestamper in the electroforming step will be simpler.

When the diffuser plate is to be used as a reflection-type diffuserplate, for example, an aluminum reflective film should bevacuum-deposited on the surface of a member on which a microlens arrayis formed, and incident light should be reflected by the aluminumsurface. Also, when the microlens array is a member formed on only onesurface of the substrate, a possible configuration is such that thelight may be incident from the mirror surface side of the substrate andreflected by the microlens array surface on which the aluminumreflective film is formed. On the other hand, a configuration in whichlight is incident from the microlens array surface on which noreflective film is formed and reflected on the mirror surface side onwhich the reflective film is formed can also be used as a diffuserplate. Further, another possible configuration may be adopted accordingto which a substrate with microlens array formed on both sides is used,the thickness of the reflective film on the incidence side is adjustedto provide a half mirror, and the back side thereof is made to have areflectance of almost 100%, and thereby a diffuser plate using twomicrolens arrays, i.e., microlens arrays provided on the front and backsurfaces can be obtained. Also, if necessary, a protective layer may becoated to protect the aluminum reflective film.

Second Embodiment

A diffuser plate according to a second embodiment will be described withreference to FIGS. 4 to 6. FIG. 4 shows a front view 60 a illustrating abasic block 60, a side view 60 b seen in the Y-axis direction, and aside view 60 c seen in the X-axis direction in the diffuser plate of thesecond embodiment. FIG. 5 is a 4A-4A′ sectional view in the diffuserplate of FIG. 4, and FIG. 6 is a 4B-4B′ sectional view in the diffuserplate of FIG. 4. In the examples of FIGS. 4 to 6, N=M=4.

The diffuser plate of the second embodiment is a transmission-typediffuser plate, and includes a first optical element 63 a having aneffective diameter “a” in the X-axis direction on one surface (+Z sidesurface) of a planar base material 61, and a second optical element 63 bhaving an effective diameter “b” in the Y-axis direction on the othersurface (−Z side surface) of the base material. Although different fromthe diffuser plate of the first embodiment in this respect, by supposingthat an optical element with an effective diameter “a” in the X-axisdirection and an effective diameter “b” in the Y-axis direction areformed through the combination of the first optical element 63 a and thesecond optical element 63 b, a periodic phase structure that has N rowsand M columns as the basic block and creates an Na×Mb two-dimensionaloptical path length difference can be treated in the same manner as inthe first embodiment.

FIG. 5 is a sectional view that illustrates an example of a crosssection passing through basic periodic structures 13, 23, 33 and 43along the X-axis. As shown in the example of FIG. 5, in the diffuserplate of the second embodiment, first optical elements 63 a each havingan effective diameter “a” in the X-axis direction are arranged atintervals based on the effective diameter, thereby constituting thebasic periodic structures 13 to 43 in the X-axis direction.

Further, FIG. 6 is a sectional view that illustrates an example of across section passing through basic periodic structures 34, 33, 32 and31 along the Y-axis. As shown in the example of FIG. 6, in the diffuserplate of the second embodiment, second optical elements 63 b each havingan effective diameter “b” in the Y-axis direction are arranged atintervals based on the effective diameter, thereby constituting thebasic periodic structures 34 to 31.

Each basic structure has raised portions for respectively creating anoptical path length difference. In the examples of FIGS. 5 and 6, afirst raised portion 62 a is formed on the first optical element 63 aside, and a second raised portion 62 b is formed on the second opticalelement 63 b side. In this case, by configuring such that the firstraised portion 62 a has a height based on the above-described basicperiodic phase difference ΔP_(X) in the X-axis direction, and the secondraised portion 62 b has a height based on the above-described basicperiodic phase difference ΔP_(Y) in the Y-axis direction, it is madepossible, through this combination, to form a periodic phase structurethat creates a predetermined optical path length difference. Since thedesign method of the structure that creates an optical path lengthdifference is the same as that of the first embodiment, the descriptionthereof will be omitted here.

A typical example of shapes of the first optical element and the secondoptical element is a lenticular lens. The shape of the lenticular lensis not particularly limited, and a reference shape is designed fromoptical physical properties (particularly, refractive index) of thematerial used for the diffuser plate and a desired diffusion angledistribution. Further, it may be a concave lens which has an invertedshape of the lenticular lens.

Further, a reflection-type diffuser plate may be made by forming areflective film such as an aluminum vapor deposition film on one of thefirst optical element and the second optical element.

In common between the diffuser plate of the first embodiment and thediffuser plate of the second embodiment, speckle noise is suppressed bygiving a periodic predetermined phase difference to respective lighttransmitted through or reflected by each optical element. Further, inthe diffuser plate of the first embodiment and the diffuser plate of thesecond embodiment, by configuring such that at least one of N and M isan integer of 3 or more, it is made possible to further mitigate theunevenness of luminance and the unevenness of color.

EXAMPLES

Hereinafter, a more detailed description will be given by usingexamples. Note that the present invention is not limited to thefollowing examples.

In the following examples, an example relating to a transmission-typediffuser plate in which a microlens array is formed on one surface of aplanar base material is shown.

<Example 1> N=M=3

Let us consider a microlens array which satisfies the condition that theexpression (3) is 0.3 or less with N=M=3. Here, as an example, supposingthat a phase difference for one period of the periodic phase structurein the X-axis direction and the Y-axis direction be ΔP_(X) and ΔP_(Y),ΔP_(X) and ΔP_(Y) are set as follows:

${\Delta\; P_{X}} = \begin{pmatrix}0 & {\frac{1}{3}\lambda} & {\frac{1}{3}\lambda}\end{pmatrix}$ ${\Delta\; P_{Y}} = \begin{pmatrix}0 & {\frac{1}{3}\lambda} & {\frac{1}{3}\lambda}\end{pmatrix}$

A phase difference ΔP for one period of a periodic phase structure inwhich the X-axis direction and the Y-axis direction are combined is setby the sum of the phase difference ΔP_(X) in the X-axis direction andthe phase difference ΔP_(Y) in the Y-axis direction, and therefore isexpressed as follows:

$\begin{matrix}{{\Delta\; P} = {\begin{pmatrix}0 & 0 & {\frac{1}{3}\lambda} \\0 & 0 & {\frac{1}{3}\lambda} \\{\frac{1}{3}\lambda} & {\frac{1}{3}\lambda} & {\frac{1}{3}\lambda}\end{pmatrix}.}} & {{Expression}\mspace{14mu}(6)}\end{matrix}$

Based on the phase difference ΔP, a ratio of the standard deviation tothe average of directivity |G|² of emitted light is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}{\sum\limits_{1}^{N}\;\left( \;{{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 0$

Therefore, the condition that the expression (3) is 0.3 or less issatisfied. The result of the diffracted light simulation at this time isshown in FIG. 11(a). Compared with FIG. 9(a), the density of thediffracted light has increased by 9 times, and it can be confirmed thatthe unevenness of luminance is reduced. The phase difference whichsatisfies the condition that the expression (3) is 0.3 or less withN=M=3 is not limited to the expression (6), and any phase difference maybe set as long as the condition that the expression (3) is 0.3 or lessis satisfied.

<Example 2> N=M=5

Let us consider a microlens array which satisfies the condition that theexpression (3) is 0.3 or less with N=M=5. Here, as an example, supposingthat a phase difference for one period of the periodic phase structurein the X-axis direction and the Y-axis direction be ΔP_(X) and ΔP_(Y),ΔP_(X) and ΔP_(Y) are set as follows:

${\Delta\; P_{X}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{Y}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0\end{pmatrix}$

A phase difference ΔP for one period of a periodic phase structure inwhich the X-axis direction and the Y-axis direction are combined is setby the sum of the phase difference ΔP_(X) in the X-axis direction andthe phase difference ΔP_(Y) in the Y-axis direction, and therefore isexpressed as follows:

$\begin{matrix}{{\Delta\; P} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0 \\{\frac{2}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{2}{5}\lambda} \\{\frac{1}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{2}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{1}{5}\lambda} \\{\frac{2}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{2}{5}\lambda} \\0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0\end{pmatrix}} & {{Expression}\mspace{14mu}(7)}\end{matrix}$

Based on the phase difference ΔP, a ratio of the standard deviation tothe average of directivity |G|² of emitted light is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}{\sum\limits_{1}^{N}\;\left( \;{{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 0$

Therefore, the condition that the expression (3) is 0.3 or less issatisfied. The result of the diffracted light simulation at this time isshown in FIG. 11(b). Compared with FIG. 9(a), the density of thediffracted light has increased by 25 times, and it can be confirmed thatthe unevenness of luminance is reduced. The phase difference whichsatisfies the condition that the expression (3) is 0.3 or less withN=M=5 is not limited to the expression (7), and any phase difference maybe set as long as the condition that the expression (3) is 0.3 or lessis satisfied.

<Example 3> N=M=7

Let us consider a microlens array which satisfies the condition that theexpression (3) is 0.3 or less with N=M=7. Here, as an example, supposingthat a phase difference for one period of the periodic phase structurein the X-axis direction and the Y-axis direction be ΔP_(X) and ΔP_(Y),ΔP_(X) and ΔP_(Y) are set as follows:

${\Delta\; P_{X}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & \frac{2}{7} & \frac{3}{7} & 0\end{pmatrix}$ ${\Delta\; P_{Y}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & \frac{2}{7} & \frac{3}{7} & 0\end{pmatrix}$

A phase difference ΔP for one period of a periodic phase structure inwhich the X-axis direction and the Y-axis direction are combined is setby the sum of the phase difference ΔP_(X) in the X-axis direction andthe phase difference ΔP_(Y) in the Y-axis direction, and therefore isexpressed as follows:

$\begin{matrix}{{\Delta\; P} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & 0 \\{\frac{3}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{7}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{3}{7}\lambda} \\{\frac{2}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{2}{7}\lambda} \\{\frac{4}{7}\lambda} & {\frac{7}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{8}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{7}{7}\lambda} & {\frac{4}{7}\lambda} \\{\frac{2}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{2}{7}\lambda} \\{\frac{3}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{7}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{3}{7}\lambda} \\0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & 0\end{pmatrix}} & {{Expression}\mspace{14mu}(8)}\end{matrix}$

Based on the phase difference ΔP, a ratio of the standard deviation tothe average of directivity |G|² of emitted light is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}{\sum\limits_{1}^{N}\;\left( \;{{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 0$

Therefore, the condition that the expression (3) is 0.3 or less issatisfied. The result of the diffracted light simulation at this time isshown in FIG. 11(c). Compared with FIG. 9(a), the density of thediffracted light has increased by 49 times, and it can be confirmed thatthe unevenness of luminance is reduced. The phase difference whichsatisfies the condition that the expression (3) is 0.3 or less withN=M=7 is not limited to the expression (8), and any phase difference maybe set as long as the condition that the expression (3) is 0.3 or lessis satisfied.

<Example 4> N=3, M=4

Let us consider a case in which N and M are different from each other,for example, a microlens array which satisfies the condition that theexpression (3) is 0.3 or less with N=3 and M=4. Here, as an example,supposing that a phase difference for one period of the periodic phasestructure in the X-axis direction and the Y-axis direction be ΔP_(X) andΔP_(Y), ΔP_(X) and ΔP_(Y) are set as follows:

${\Delta\; P_{X}} = \begin{pmatrix}0 & {\frac{1}{3}\lambda} & {\frac{1}{3}\lambda}\end{pmatrix}$ ${\Delta\; P_{Y}} = {\begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda}\end{pmatrix}.}$

A phase difference ΔP for one period of a periodic phase structure inwhich the X-axis direction and the Y-axis direction are combined is setby the sum of the phase difference ΔP_(X) in the X-axis direction andthe phase difference ΔP_(Y) in the Y-axis direction, and therefore isexpressed as follows:

$\begin{matrix}{{\Delta\; P} = \begin{pmatrix}0 & {\frac{4}{12}\lambda} & {\frac{4}{12}\lambda} \\{\frac{3}{12}\lambda} & {\frac{7}{12}\lambda} & {\frac{7}{12}\lambda} \\{\frac{6}{12}\lambda} & {\frac{10}{12}\lambda} & {\frac{10}{12}\lambda} \\{\frac{3}{12}\lambda} & {\frac{7}{12}\lambda} & {\frac{7}{12}\lambda}\end{pmatrix}} & {{Expression}\mspace{14mu}(9)}\end{matrix}$

Based on the phase difference ΔP, a ratio of the standard deviation tothe average of directivity |G|² of emitted light is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( {{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 0$

Therefore, the condition that the expression (3) is 0.3 or less issatisfied. The result of the diffracted light simulation at this time isshown in FIG. 11(d). Compared with FIG. 9(a), the density of thediffracted light has increased by 12 times, and it can be confirmed thatthe unevenness of luminance is reduced. Any phase difference may be setnot only at N=3 and M=4, but also at any value of N and M, if thecondition that the expression (3) is 0.3 or less is satisfied.

<Comparative Example 1>2×2 Array

Let us now consider a 2×2 array as illustrated in Patent Literature 4.In this example, it is said to be preferable that the basic block be a2×2 array defined by the sum of the respective optical path lengthdifferences caused by the periodic phase structure in the x-directionand the periodic phase structure in the y-direction, and the opticalpath length difference be set to ¼ times the wavelength. That is,supposing that phase differences for one period of the periodic phasestructures in the X-axis direction and the Y-axis direction be ΔP_(X)and ΔP_(Y), ΔP_(X) and ΔP_(Y) are set as follows:

${\Delta\; P_{N}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{M}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda}\end{pmatrix}$

A phase difference ΔP for one period of a periodic phase structure, inwhich the X-axis direction and the Y-axis direction are combined, is setby the sum of the phase difference ΔP_(X) in the X-axis direction andthe phase difference ΔP_(Y) in the Y-axis direction, and therefore isexpressed as follows:

$\begin{matrix}{{\Delta\; P} = {\begin{pmatrix}0 & {\frac{1}{4}\lambda} \\{\frac{1}{4}\lambda} & {\frac{2}{4}\lambda}\end{pmatrix}.}} & {{Expression}\mspace{14mu}(10)}\end{matrix}$

Based on the phase difference ΔP, a ratio of the standard deviation tothe average of directivity |G|² of emitted light is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( {{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 0$

Therefore, this 2×2 array satisfies the condition that the expression(3) is 0.3 or less. A result of diffracted light simulation of amicrolens array to which this 2×2 array is applied is shown in FIG.12(a). Compared with FIG. 9(a), the density of the diffracted light hasincreased, and thus the unevenness of luminance is reduced. However,even though the level of the phase difference provided is the same asthat of Example 1, the density of the diffracted light is smaller thanthat of FIG. 11(a), so that the effect of reducing the unevenness ofluminance is inferior to that of the present invention.

<Comparative Example 2>4×4 Array (Patent Literature 4)

Let us now consider a 4×4 array as illustrated in Patent Literature 4.In this example, it is said to be preferable that the basic block be a4×4 array defined by the sum of the respective optical path lengthdifferences caused by the periodic phase structure in the x-directionand the periodic phase structure in the y-direction, and the opticalpath length difference be set to ½ times the wavelength. That is, if thephase differences for one period of periodic phase structures in theX-axis direction and the Y-axis direction be ΔP_(X) and ΔP_(Y), ΔP_(X)and ΔP_(Y) are set as follows:

${\Delta\; P_{X}} = \begin{pmatrix}0 & 0 & {\frac{1}{2}\lambda} & {\frac{1}{2}\lambda}\end{pmatrix}$ ${\Delta\; P_{Y}} = \begin{pmatrix}0 & 0 & {\frac{1}{2}\lambda} & {\frac{1}{2}\lambda}\end{pmatrix}$

A phase difference ΔP for one period of a periodic phase structure inwhich the X-axis direction and the Y-axis direction are combined is setby the sum of the phase difference ΔP_(X) in the X-axis direction andthe phase difference ΔP_(Y) in the Y-axis direction, and therefore isexpressed as follows:

$\begin{matrix}{{\Delta\; P} = \begin{pmatrix}0 & 0 & {\frac{1}{2}\lambda} & {\frac{1}{2}\lambda} \\0 & 0 & {\frac{1}{2}\lambda} & {\frac{1}{2}\lambda} \\{\frac{1}{2}\lambda} & {\frac{1}{2}\lambda} & 0 & 0 \\{\frac{1}{2}\lambda} & {\frac{1}{2}\lambda} & 0 & 0\end{pmatrix}} & {{Expression}\mspace{14mu}(11)}\end{matrix}$

Based on the phase difference ΔP, a ratio of the standard deviation tothe average of directivity |G|² of emitted light is obtained as follows:

$\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( {{G}^{2} - {Ave}} \right)^{2}}}}}{Ave} = 1.73$

Therefore, this 2×2 array does not satisfy the condition that theexpression (3) is 0.3 or less. A result of diffracted light simulationof a microlens array to which this 2×2 array is applied is shown in FIG.12(b). Compared with FIG. 9(a), the density of the diffracted light hasincreased, and thus the unevenness of luminance is reduced. However,compared with Example 1 of FIG. 11(a), the density of diffracted lightis small so that the effect of reducing the unevenness of luminance isinferior to that of the present invention.

This application claims the priority based on Japanese PatentApplication No. 2019-011212 filed on Jan. 25, 2019, the entiredisclosure of which is incorporated herein by reference.

REFERENCE SIGNS LIST

-   -   10 Basic periodic structure; 11 to 44 Basic periodic structure        in n rows and m columns in a basic block; 50 Basic block; 51        Base material; 52 Raised portion; 53 Optical element; 60 a to c        Basic blocks; 61 Base material; 62 a to b Raised portions; 63 a        First optical element; 63 b Second optical element; 71, 72        Optical path length difference; 100 Diffuser plate.

1. A transmission-type or reflection-type diffuser plate, comprising aplanar base material on which an X-axis and a Y-axis which areorthogonal to each other are defined in a plane direction, wherein anoptical element having an effective diameter of “a” in an X-axisdirection, and an effective diameter of “b” in a Y-axis direction isprovided on one surface of the planar base material; or a first opticalelement having an effective diameter of “a” in the X-axis direction isprovided on one surface of the planar base material, and a secondoptical element having an effective diameter of “b” in the Y-axisdirection is provided on the other surface of the planar base material,and an optical element having an effective diameter of “a” in the X-axisdirection, and an effective diameter of “b” in the Y-axis direction isformed by combining the first optical element and the second opticalelement; an a×b two-dimensional basic periodic structure is constitutedby a plurality of the optical elements being disposed in the X-axisdirection and the Y-axis direction at intervals respectively based onthe effective diameters; each basic periodic structure has a structurethat creates an optical path length difference, respectively; thestructure that creates the optical path length difference has an Na×Mbtwo-dimensional periodic phase structure in which a basic block has Nrows and M columns (at least one of M and N is an integer of 3 or more)including N optical elements in the X-axis direction and M opticalelements in the Y-axis direction; and the diffuser plate is configuredsuch that if a phase structure in the n-th row and the m-th column inthe basic block is denoted by P_(nm), and if a basic periodic phasedifference ΔP_(X) in the X-axis direction and a basic periodic phasedifference ΔP_(Y) in the Y-axis direction are expressed as the followingexpressions (1) and (2), the Pnm is expressed as P_(n1)+P_(1m); andΔP _(X)=(P ₁₁ P ₂₁ . . . P _(N1))  Expression (1)ΔP _(Y)=(P ₁₁ P ₁₂ . . . P _(1M))  Expression (2) if complextransmittance or complex reflectance of the optical element in the n-throw and the m-th column in the basic block is denoted by g(n/λ, m/λ),and directivity is represented by square of the absolute value ofFourier transform G(sin θ_(n), sin θ_(m)) of complex transmittance orcomplex reflectance, a ratio of standard deviation to average of thedirectivity expressed by the following expression (3) is 0.3 or less.$\begin{matrix}\frac{\sqrt{\frac{1}{NM}{\sum\limits_{1}^{M}\;{\sum\limits_{1}^{N}\left( \left. {{G_{N,M}\left( {{\sin\;\theta_{n}},{\sin\;\theta_{m}}} \right.}^{2} - {Ave}} \right)^{2} \right.}}}}{Ave} & {{Expression}\mspace{14mu}(3)}\end{matrix}$ (In the expression (3), Ave is an average value of |G(sinθ_(n), sin θ_(m))|² of each optical element in the basic block.)
 2. Thediffuser plate according to claim 1, wherein the ratio of the standarddeviation to the average of the directivity expressed by the expression(3) is 0.1 or less.
 3. The diffuser plate according to claim 1, whereinthe ratio of the standard deviation to the average of the directivityexpressed by the expression (3) is
 0. 4. The diffuser plate according toclaim 1, wherein the N and M are each independently any of 3, 4, 5, 7,and 8, and when a wavelength of incident light is λ, a basic periodicphase difference ΔP_(X) in the X-axis direction and a basic periodicphase difference ΔP_(Y) in the Y-axis direction are independently one ofthe following ΔP_(A). ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & {\frac{1}{3}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & 0 & {\frac{2}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & 0 & {\frac{3}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{4}\lambda} & {\frac{2}{4}\lambda} & {\frac{1}{4}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{1}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{1}{5}\lambda} & {\frac{2}{5}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & 0 & {\frac{2}{5}\lambda} & {\frac{2}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{1}{5}\lambda} & 0 & {\frac{3}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{4}{5}\lambda} & {\frac{1}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{3}{5}\lambda} & {\frac{2}{5}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{1}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{2}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & 0\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & 0 & {\frac{4}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{4}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{1}{7}\lambda} & 0 & {\frac{5}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{5}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{2}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{1}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{1}{7}\lambda} & 0 & {\frac{2}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{0}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{1}{7}\lambda} & {\frac{2}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{2}{7}\lambda} & 0 & {\frac{3}{7}\lambda} & {\frac{4}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{3}{7}\lambda} & {\frac{2}{7}\lambda} & 0 & {\frac{4}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{6}{7}\lambda} & {\frac{5}{7}\lambda} & {\frac{3}{7}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & 0 & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & 0 & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & 0 & {\frac{2}{8}\lambda} & 0 & 0 & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & 0 & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & 0 & {\frac{7}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{7}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{5}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{1}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{3}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{7}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{7}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{1}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{1}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{5}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{6}{8}\lambda} & {\frac{1}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & 0 & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & 0 & {\frac{6}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{6}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{6}{8}\lambda} & 0 & {\frac{6}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{2}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{2}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{2}{8}\lambda} & 0 & {\frac{4}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{8}\lambda} & 0 & {\frac{5}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{3}{8}\lambda} & {\frac{4}{8}\lambda} & {\frac{5}{8}\lambda}\end{pmatrix}$ ${\Delta\; P_{A}} = \begin{pmatrix}0 & {\frac{3}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{3}{8}\lambda} & 0 & {\frac{7}{8}\lambda} & {\frac{2}{8}\lambda} & {\frac{7}{8}\lambda}\end{pmatrix}$
 5. The diffuser plate according to claim 4, wherein the λis 630 nm.
 6. The diffuser plate according to claim 4, wherein the λ is530 nm.
 7. The diffuser plate according to claim 4, wherein the λ is 580nm.